I make fun of the major cable news networks a lot, sometimes even devoting entire posts to their amusing errors. I’m also fairly dismissive of the way they put sensationalism and minutiae over real news and events which affect millions of people. I think it’d be nice if the American consumer demanded more from their news sources.

But in the interest of fair play, I should also recognize when news organizations are doing a particularly good job highlighting big issues, educating the public about the world outside their familiar communities, or otherwise providing high quality journalism that would be impossible to replicate on blogs or Twitter. There are reasons these organizations are filled with talented professionals and given large budgets–and those reasons are not celebrity obituaries or hours of uninformed analysis about politicians’ wardrobes.

CNN.com has been putting out some really great reporting lately, and I thought it worthy of recognition. A few examples:

This investigative report on the state of slavery in Mauritania is truly exceptional. It’s well-written, well-researched, and the photographs are as compelling as both the personal stories and larger statistics. A small team of professionals literally risked their lives to bring to light information about one of slavery’s last bastions on this planet, and I consider their undertaking nothing less than a significant service to humanity.

This story of escaped North Koreans provides a badly needed human narrative and perspective to the increasingly important discussion about dealing with dictatorships. It’s important to remember that an entire country led by a dictator cannot be our enemy. The United States and the citizens of North Korea have, in fact, the same enemy.

A US Naval Lieutenant and Friend of the Blog, Ben at Think Like a Fox, has an interesting response to my previous post, with which I’m in complete agreement. That he seems to think we’re in some slight disagreement suggests I need to clarify the “Mixed Strategy” approach I espoused.

A mixed strategy, in game theory, employs some randomization, but that doesn’t mean everything about it is random. It could be flipping a coin between two specific strategies. It could mean randomly drawing from a more complicated probability distribution as an input to the decision. But the randomization is strategically chosen to produce the best expected outcomes.

The reason I think there should be a random element in Iron Dome unit deployment is that playing what game theorists call a “pure strategy” makes one predictable. A pure strategy doesn’t have to be a specific deployment, but it would mean a specific strategy for deployment, a “best response function” to use the technical term. That is, for a given set of situational inputs, a pure strategy will kick out a response without any randomness. Like any function, identical inputs mean identical outputs (or adjusting for a real-world situation, similar inputs yield similar outputs). And that makes someone predictable, at least eventually. An intelligent opponent could easily take advantage of that.

So a mixed strategy would involve randomly choosing between several good strategies. If all the “good strategies” have some things in common–such as the protection of the most important locations in the entire country, as my counterpart suggests–then so be it. It could be that some things are so important you don’t care that Hamas knows they’re protected. That’s fine.

But randomly moving from one good strategy to another good strategy would create a great deal of uncertainty on the part of the attackers. Hamas might not want to take a chance that most of their attacks will be thwarted. And as a result, they’ll deliberately launch less effective attacks with a higher probability of actually doing anything at all.

An Illustrative Example

To build intuition about mixed strategies, consider this extremely simplified example. Israel has one Iron Dome unit, 3 important locations to defend (a military target, a civilian target, and a mixed target), and 1 less important location to defend. Hamas can launch 2 rocket attacks this week. If Israel is playing a pure strategy, Hamas knows that in all likelihood, two of the important locations will be defended. If the pure strategy prioritizes strategic targets, the civilian location will be undefended. If the pure strategy prioritizes civilian protection, the military target will be undefended. [In this case, we’ll assume that “strategy” only involves protecting military or civilian targets; it’s obviously more complicated in reality.]

Hamas will quickly see that it can use its two rocket attacks to guarantee exactly one of those important locations will be hit (NOTE: Hamas can guarantee that without having a clue which pure strategy Israel chose). But now say Israel plays a mixed strategy where it introduces a random element: at any given time, 2 of the 3 important locations will be defended–completely at random, no strategy. Now, if Hamas attacks any two of those locations, there’s a 1-in-3 chance they’ll be completely unsuccessful. If Hamas is risk averse, or doesn’t want to lose momentum, or feels like it’s more important to hit somewhere than risk hitting nothing (and Hamas certainly has shown that mentality to be prevalent), then the logical choice will be to divert to less important targets, meaning fewer casualties, less damage, and/or a higher probability of getting caught.

And that, in a nutshell, is why I support a mixed strategy on Israel’s part when it comes to deploying its Iron Dome units.

Iron Dome units are essentially expensive and portable anti-rocket defense platforms which stop a good percentage of rockets fired at the coverage area (around 90% if some reports are to be believed). This is a great new defensive technology, and Israel will probably make quite a few of them. But, because of the cost, they won’t make enough to blanket the entire country with coverage.

This leaves strategists and policy makers one important question: where do you put the units? Which areas do you defend, and which do you leave vulnerable?

Quoted in the CNN article (linked above) is a former Israeli ambassador who says:

“The most important question is how would the Iron Dome affect the decisions of Hamas leaders and their Iranian supporters? While Hamas rockets are aimed primarily to target civilians and terrorize the Israeli home front, a secondary and just important aim is to hit strategic sites in the future. Eliminating the ability to hit strategic targets may lead Hamas to rethink the efficiency of acquiring the rockets it has used in the past.”

His contention is that once Israel protects its most strategically valuable targets, Hamas won’t buy as many rockets, and attacks will go down or disappear. I find this to be an incredibly dangerous assumption. It’s a pretty fundamental rule in public policy (and economics, and behavioral economics) that people respond to incentives, and not always in predictable ways. So I spent some time trying to figure out how Hamas would respond to Israel’s deployment of Iron Domes to protect strategic targets.

First, if Israel is smart, they won’t make it publicly known where these devices are. That way Hamas can’t just look at a map and decide to attack the most valuable non-protected area. So the terrorists have a little uncertainty to work with (for you game theory fans out there, I’m modeling this as a Bayesian game where Hamas puts probabilities of protection on targets that impacts their expected results of an attack).

Also, keep in mind, Hamas has two economic forces at play in their rocket supply chain. The first is simple supply and demand. If Hamas wants one rocket, that’s easier and cheaper to get than their hundredth rocket. So they keep buying rockets until the cost of the rocket outweighs how much they value the destruction they’ll cause with it (or until they run out of the ability to buy rockets–if this is the case, Iron Domes may have no impact whatsoever on rocket acquisition). So lowering the value of rocket attacks may have an impact, but then again, it might not.

The second economic reality Hamas faces with rockets is diminishing marginal “returns” on their attacks as they launch more rockets at the same type of target. Presumably they have some very high rated military and civilian targets and some others which are less important for them to attack. So if all of the sudden their military targets go off the table, and they have extra rockets lying around, they’ll just pick more civilian targets to attack.

That’s an oversimplification, of course, and may or may not be true. But there’s no way around it: now that they have to put expected probability of protection on each of these targets, the rankings are going to change. Specifically, targets which they expect to be less protected increase in desirability to attack. And if Israel is putting the Iron Domes on strategic targets, it makes your average residential neighborhood much more tempting. (Yes, Israel could be lying, but such a deception would be discovered very quickly.)

So one big question I’d have for Israeli officials: how do you expect Hamas terrorist in possession of rockets to react to your new policies? Because the game is changing. They can’t set up Iron Domes in areas where the most rockets were fired 2 years ago and expect Hamas to keep firing rockets into protected spaces.

And this begs another question, which was probably obvious right from the start: What’s the optimal deployment of Iron Dome units? I’m not sure yet, and I’m certainly not a military strategy expert, but I’d want to at least evaluate a few different options:

Out-in-the-Open: Instead of protecting targets based on value, protect targets based on how easy they are to hit. If you leave vulnerable high-rated targets which can only be hit from a few locations, it’s easier to catch terrorists and fight back.

Protect the LEAST strategic targets. Rocket attacks aren’t very accurate, and their biggest accomplishment is causing fear. They’re not very effective at diminishing military capabilities. (Embedded in this strategy is an ethical question that’s worth raising but which I don’t feel qualified to answer: should you protect soldiers at the expense of increased risk to civilians? Should you protect civilians and leave your fighting men and women–those most at risk in their daily lives–unprotected?)

Random deployment. No, this isn’t as crazy as it sounds. You randomly select from good strategies with some weighted algorithm, and re-select every day/week/month. In Game Theory, this is called a mixed strategy, and it’s often optimal for a lot of reasons. In this case, if you have a pure strategy (that is, do the same thing all the time or respond based on the same criteria), you can become predictable, which is a horrible thing to be in a combat situation. The mobility of Iron Dome units makes this possible, but there are transaction costs (a few hours of them protecting nobody while in transit) to consider. I think this may be my favorite, as I believe it has the highest chance of doing what the Israeli ambassador wants the Iron Dome to do: significantly reduce attempted Hamas rocket attacks.

This type of situation is a lot more complicated than we’re often led to believe, and questions like “What’s the best policy?” can only be answered after an entire society has a frank and open discussion about its values and priorities. So…go have that discussion. Seriously, stop reading blogs.